Statistics of current activity fluctuations in asymmetric flow with exclusion

TL;DR

This paper analyzes the current activity fluctuations in the one-dimensional TASEP model, deriving exact moments and distributions, and confirming results with numerical simulations.

Contribution

It provides new closed-form expressions for moments and distributions of activity fluctuations in TASEP with various boundary conditions.

Findings

Exact expressions for the first three moments of activity distribution.

Numerical simulations confirm analytical results with high accuracy.

Asymptotic approximations for probability distributions are also provided.

Abstract

We consider steady-state current activity statistics for the one-dimensional totally asymmetric simple exclusion process (TASEP). With the help of the known operator algebra (for general open boundary conditions), as well as general probabilistic concepts (for the periodic case), we derive and evaluate closed-form expressions for the lowest three moments of the probability distribution function. These are confirmed, to excellent degree of accuracy, by numerical simulations. Further exact expressions and asymptotic approximations are provided for probability distributions and generating functions.